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3 years ago

The displacement of a particle on a vibrating string is given by the equation s(t)=3+ \frac{1}{5} sin (3πt)

Mathematics

1 answer:

aliina [53]3 years ago

6 0

Answer:

$v(t)=\dfrac{3\pi}{5}\cos{(3\pi t)}$

Step-by-step explanation:

The velocity is the derivative of position.

$s(t)=3+ \dfrac{1}{5} \sin{(3\pi t)}\\\\v(t)=s'(t)=\dfrac{1}{5}(3\pi)\cos{(3\pi t)}\\\\\boxed{v(t)=\dfrac{3\pi}{5}\cos{(3\pi t)}}$

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Q # 1 Graph the function Y = |X + 2| - 3

Svetllana [295]

First of all we know the Absolute Value Function that is:

$\left | x \right |= \left \{ {{x \ \ \ \ x \geq 0} \atop {-x \ \ \ \ x\ \textless \ 0}} \right.$

This is called the Parent Function of the Absolute Value Function.

From the equation:

$y=\left | x+2 \right |-3$

The term:

$\left | x+2 \right |$

means that the the Parent Function is shifted two units to the left.

On the other hand, the term:

$-3$

means that the function $\left | x+2 \right |$ is shifted three units downward. So the result is the graph shown below

4 0

3 years ago

Read 2 more answers

Beatrice buys a dishwasher for her new house. The price of the dishwasher is D dollars, and she pays an additional 2% tax. Match

Leya [2.2K]

I think it's D + .2 = ? i'm not sure but it might be something like that

6 0

4 years ago

Select the correct answer from each drop-down menu.

Alenkasestr [34]

Answer:

The points of intersections are: (1.5 , 1.25) and (4 , 0)

Step-by-step explanation:

Given:

y = x² - 6x + 8 ⇒ (1)

2y + x = 4 ⇒ (2)

And required the solution of the system of equations.

By graphing the system of equations, the points of intersections are:

(1.5 , 1.25) and (4 , 0)

See the attached figure.

Another solution:

By substitution of y from the second equation at the first equation.

From (1) ⇒ y = 0.5 (4-x)

At (2): and solve for x

0.5 ( 4 - x ) = x² - 6x + 8 ⇒ multiply both sides by 2

4 - x = 2x² - 12x + 16

2x² - 12x + 16 + x - 4 = 0

2x² - 11x + 12 = 0

The general solution of the quadratic equation:

$x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}$

so, a = 2 , b = -11 and c = 12

∴ $x=\frac{-(-11) \pm \sqrt{(-11)^2-4*2*12} }{2*2}=\frac{11 \pm \sqrt{25} }{4} =\frac{11 \pm 5}{4} \\x = \frac{11+5}{4} = \frac{16}{4}=4\\ OR \ x = \frac{11-5}{4}=\frac{6}{4}=1.5\\$

∴ at x = 4 ⇒ y = 0.5 (4-x) = 0.5 * 0 = 0

And at x = 1.5 ⇒ y = 0.5 (4-x) = 0.5 * ( 4 - 1.5 ) = 0.5 * 2.5 = 1.25

So, the solution are the points (4,0) and (1.5 , 1.25)

6 0

3 years ago

2.16 (the 6 is repeating) as a fraction (no improper fractions)

serg [7]

Answer:

2 4/25

Step-by-step explanation:

First, I made the decimal into 2 16/100. Then, keep simplifying the 16/100 until it is fully simplified.

6 0

4 years ago

Point C is the center of the circle. If angle ACB measures (3x + 1)° and arc AB measures (2x + 7)°, find x

Feliz [49]

$m(\widehat{ACP}) = m(\overset{\frown}{AB}) \\ \\ 
\Longrightarrow~~~(3x+1)^o = (2x+7)^o \\ \\ 
3x+1 = 2x+7 \\ \\ 
3x - 2x = 7-1 \\ \\ 
\boxed{x = 6^o }$

7 0

4 years ago